You are sitting at 0 stacks the moment you activate IB. If you are taking some 9000 damage in a short period of time as people indicate you do in Coil, it's very easy to see how War fall behind. In terms of pure instantaneous survivability, the War and Pal are equal. That spike damage is not instantaneous. It probably occurs over a 2-3ish timeframe. Pal has a 8.7% healing advantage during this. War uses IB after it. Let's just say it heals for 2000. Healing advantage Pal has spikes significantly. 2000 is ~2 auto attacks. Some follow up is mitigated. That's true. But, the incoming healing is greatly reduced compared to Paladin. During the recovery from burst phase, damage is still incoming and I'd bet money there are additional (less severe) burst spikes here the Pal has a huge advantage.

IB is a disadvantage because a War is already at a healing disadvantage compared to a Pal and when used that gap explodes.